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isothermalwind

v6	v7
9	9	Substitute (3) and (2) into (1) and assume the wind is in steady state, we can get:
10	10
11		$\frac{1}{u}\frac{du}{dt}=(\frac{2a^2}{r}-\frac{GM}{r^2})/(u^2-a^2)$ (4)
	11	$\frac{1}{u}\frac{du}{dr}=(\frac{2a^2}{r}-\frac{GM}{r^2})/(u^2-a^2)$ (4)
12	12
13	13	$u=a$ is a singular point and $\frac{2a^2}{r}-\frac{GM}{r^2}=0$ is critical point. If the wind is to experience constant acceleration, u will exceed a at some radius such that the equation become singular. Therefore the reasonable picture for the constant accelerating wind is that numerator goes to 0 as the denominator goes to 0.